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Due to the short decohorence time of qubits available in the NISQ-era, it isessential to pack (minimize the size and or the depth of) a logical quantumcircuit as efficiently as possible given a sparsely coupled physicalarchitecture. In this work we introduce a locality-aware qubit routingalgorithm based on a graph theoretic framework. Our algorithm is designed forthe grid and certain "grid-like" architectures. We experimentally show thecompetitiveness of algorithm by comparing it against the approximate tokenswapping algorithm, which is used as a primitive in many state-of-the-artquantum transpilers. Our algorithm produces circuits of comparable depth(better on random permutations) while being an order of magnitude faster than atypical implementation of the approximate token swapping algorithm.

Locality-aware Qubit Routing for the Grid Architecture